A wavelet multiresolution interpolation Galerkin method with effective treatments for discontinuity for crack growth analyses. (15th February 2020) - Liu, Xiaojing; Liu, G.R.; Wang, Jizeng; Zhou, Youhe
Highlights: A novel and truly meshfree method is proposed to study the growth of cracks. Singular stress fields are captured by a purely linear displacement method with multiresolution enhancement. Robust nodal refining model is available for generating local multiresolution refinement. Local refinement is automatically updated without changing other nodes. A high degree of path-independence of J-integral is achieved. Abstract: A wavelet multiresolution interpolation Galerkin method (WMIGM) with effective algorithm for treatments on the discontinuity of cracks is developed to handle the growth of cracks. In our WMIGM, two robust nodal refining models of multiresolution enhancement are proposed to effectively control the generation of local nodes around the crack tips for capturing the singular stress fields. With our local multiresolution refinement algorithm, these local nodes are automatically generated and/or moved with ease, which will not affect the other nodes. The formulation of the proposed WMIGM is presented in detailed. Several problems of both stationary and growing cracks are studied to validate the present method. Results demonstrate that the present WMIGM possesses an excellent accuracy in both estimating stress intensity factors and tracing crack growth paths, as well as a strong stability against irregular nodal distribution with extremely large ratio of the maximum grid size to the minimum in the problem domain.